1. Field of the Invention
The present invention relates to a waveform displaying method and a waveform analyzing apparatus for use in the evaluation of a deep level that is present in either a semiconductor device such as a transistor, a diode, or the like which is mounted on a semiconductor substrate of gallium arsenide, for example, or the semiconductor substrate.
2. Description of the Related Art
It is known in the art that in various semiconductor devices including transistors and diodes which are made of semiconductors including gallium arsenide (GaAs), the characteristics of the devices suffer various parasitic effects when a deep level in the forbidden band gap that is present in a semiconductor substrate or on the surface thereof captures or emits a carrier (electrons or holes). For example, the deep level present in the conduction region of a device captures or emits a carrier, resulting in a delay of the response of a current flowing through the device, a junction capacitance, and a threshold voltage.
The capture of a carrier by the deep level depends on the concentration of a free carrier, and is difficult to analyze. The emission of a carrier from the deep level is not governed by the free-carrier concentration because the destination band's free-carrier concentration is usually considerably lower than the effective density of states. The ratio of the amount of carrier emitted from the deep level to the amount of carrier remaining in the deep level per unit time, i.e., the emission rate, is substantially constant. The amount of carrier that remains in the deep level is reduced exponentially with time.
If the amount of carrier emitted from the deep level is proportional to the rate at which the current varies, the current will also vary exponentially. An exponential function indicative of the change in the amount of carrier held by the deep level, or the change in the current is proportional to: EQU exp(-e.sub.n .multidot.t) (1)
where e.sub.n is the carrier emission rate. The emission rate e.sub.n itself depends on the temperature. If the carrier is an electron, then the carrier emission rate e.sub.n is expressed by the following simple equation: EQU e.sub.n =N.sub.c t.sub.th .sigma..sub.n .multidot.exp(.multidot.E.sub.T /kT)(2)
where N.sub.c is the effective density of states of the electrons which is proportional to the (3/2)th power of the temperature T, and v.sub.th is the thermal velocity of the electrons which is proportional to the (1/2)th power of the temperature T. Therefore, the carrier emission rate depends on the product of an exponential function of (-1/T) and square of the temperature T. In equation (2), E.sub.T represents the activation energy of the deep level, and .sigma..sub.n the capture cross-section. The same equation is satisfied when the carrier is a hole. To determine these parameters, the waveform of a current response or the like is analyzed according to equation (1) to find the carrier emission rate e.sub.n at a certain temperature, and the temperature-dependency thereof is then applied to equation (2) to obtain the activation energy E.sub.T of the deep level and the capture cross-section .sigma..sub.n. For the actual determination of the relationship between the temperature T and the carrier emission rate e.sub.n from the exponential function ( 1), there have been available the methods known as DLTS (Deep Level Transient Spectroscopy) and ICTS (Isothermal Capacitance Transient Spectroscopy).
ICTS is a process for determining the carrier emission rate e.sub.n at a temperature T, given as a set condition, as shown in the flowchart of FIG. 1 in the accompanying drawings. Specifically, at a temperature T, the waveform of a response is continuously recorded from the time a step input is applied, and a time t.sub.max is found where the product of the differential coefficient derivative after t seconds and the time t is a maximum (of a peak value), with the reciprocal of the time t.sub.max thus found being determined as the carrier emission rate e.sub.n.
According to DLTS, a temperature T for achieving a carrier emission rate e.sub.n, given as a set condition, is determined as shown in the flowchart of FIG. 2 in the accompanying drawings. Actually, a certain time window t.sub.w (=1/e.sub.n) is selected, and the product of the differential coefficient derivative of the response waveform at the time and t is recorded while the temperature T varies in order to find the temperature T.sub.max where the signal indicative of the product is a maximum (of a peak value).
In either DLTS or ICTS, it has been customary to vary the condition a plurality of times (the temperature T for ICTS and the time window t.sub.w for DLTS) to grasp the relationship between the carrier emission rate e.sub.n and the temperature T for obtaining parameters of the deep level using equation (2). Finally, parameters such as E.sub.T, .sigma..sub.n, etc. are compared with those of the literature to identify the deep level.
However, the conventional measurements using DLTS or ICTS have been complex as it is necessary to repeat the setting of the condition and the sweeping of the temperatures to determine the peak a plurality of times.
According to DLTS or ICTS, a spectral maximum (peak) must be determined on the assumption that the response waveform is represented by an exponential function. Such a procedure is easy if the device being measured contains a very distinct, single deep level. However, if the device being measured contains a plurality of deep levels or a peak is not distinct but spread, the above procedure cannot easily be accomplished. To determine an activation energy or the like from spectra measured under different set conditions, it has been necessary to correlate the peaks of the spectra correctly with each other. In reality, when the energy of a deep level is determined according to equation (2), a large error of up to 0.2 eV, for example, may be produced, resulting in incorrect identification of the deep level.